Physically Unclonable Function Circuits and Methods of Performing Key Enrollment in Physically Unclonable Function Circuits

ABSTRACT

A key enrollment method of a physically unclonable function (PUF) circuit including a plurality of PUF cells includes receiving a first level key from PUF cells, performing bit encoding on the first level key using a bit coding table based on Hamming weights of a plurality of bits in the first level key to generate a second level key, storing first helper data associated with the second level key in a non-volatile memory, performing block encoding on the second level key using an error correction code to generate a third level key, and storing second helper data associated with the third level key in the non-volatile memory.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims for priority under 35 U.S.C. §119 toKorean Patent Application No. 10-2014-0168505 filed Nov. 28, 2014, theentire contents of which are hereby incorporated by reference.

BACKGROUND

Embodiments of the inventive concepts described herein relate tophysically unclonable function (PUF) circuits and methods of performingkey enrollment in PUF circuits.

Cryptographic keys (or simply “keys”) ay be stored in electroniccircuits, such as memory circuits. To prevent a key from being extractedby a physical attack, a circuit that stores the key may be configured tosense when a physical attack is occurring and to react to the attack byblocking the supply of power to the circuit or by destroying thecircuit. The use of the sensors results in increasing process cost andmay require the formation of new sub-channels in the circuit that maythemselves be susceptible to attack. Current research is directed to thedesign of logic circuits that act like a fingerprint, i.e. digitalcircuits including logic implemented therein that generates keys withoutstoring keys as data. PUF technology is representative of suchapproaches.

A PUF circuit is a circuit that takes advantage of the fact that wiredelay and/or gate delay may differ slightly from one device to the nextin the same circuit due to slight variations in process conditionsduring the manufacturing process. A PUF circuit may be implemented usingsmall gate logic and may generate a random output. Delay differences dueto variations in the process conditions may make it difficult toconfigure a circuit which has the same output value even if the PUFcircuit is physically copied.

A PUF circuit may be classified as a ring oscillator type that uses adelay loop or an arbiter type that a switching circuit. Additionally, aPUF circuit may be implemented by using these two types together.

A PUF circuit is a small-sized circuit that is extremely difficult toduplicate. However, characteristics of the PUF circuit that make itunclonable may also make the circuit output different values due toslight variations in operating conditions. That is, the samecharacteristics of PUF circuits that make them difficult to clone alsomake them susceptible to generating incorrect output values. Addingerror correction circuitry to a PUF circuit may help to prevent thisphenomenon. However, doing so may result in adding additional circuitryto the PUF circuit and/or reducing the randomness of the data output bya PUF circuit.

SUMMARY

Embodiments of the inventive concepts provide PUF circuits that do notuse random bits and key enrollment methods for PUF circuits.

One aspect of embodiments of the inventive concepts is directed to a keyenrollment method of a PUF circuit that includes receiving a first levelkey from the PUF cells, the first level key comprising a plurality ofkey values, each of the key values comprising a plurality of bits,performing bit encoding on the first level key using a bit coding tablebased on Hamming weights of the plurality of bits in the key values ofthe first level key to generate a second level key, storing first helperdata associated with the second level key in a non-volatile memory,performing block encoding on the second level key using, an errorcorrection code to generate a third level key, and storing second helperdata associated with the third level key in the non-volatile memory.

Each of the PUF cells may include at least one of a PUF cell based on atransistor threshold voltage, an arbiter-based PUF cell, aring-oscillator-based PUF cell, a memory-based PUF cell, and a thermal-or laser-reconfigurable PUF cell.

Each of the PUF cells may include a plurality of nit cells configured tooutput a plurality of bit values.

The bit coding table may include a PUF output value for each of the PUFcells, a key value based on a Hamming weight of the PUF output value, amask data value configured to generate a predetermined valuecorresponding to the key value when the mask data value may be XORedwith the PUF output value, and a helper data value associated with themask data value.

The predetermined value may include a bit stream of all bits of “1” or“0” and may be configured to correct an error in a PUF output value ofeach of the PUF cells according majority decision in a bit decodingprocess.

The helper data value may include at least a part of the mask datavalue.

In some embodiments, the key value may be “1” when the Hamming weightmay be an even number, and the key value may be “0” when the Hammingweight may be an odd number. In other embodiments, the key value may be“0” when the Hamming weight may be an even number, and the key value maybe “1” when the Hamming weight may be an odd number.

The second helper data ay be not masked by mask data in the blockingencoding.

The key enrollment method may further include masking the second helperdata using a part of the second level key.

The key enrollment method may be initiated in response to a request of auser to a device including the PUF circuit.

A method of performing key generation for a physically unclonablefunction (PUF) circuit according to further embodiments includesreceiving a first level key from PUF cells, receiving first helper datafrom a non-volatile memory, performing bit decoding on the first levelkey using a bit coding table based on Hamming weights and the firsthelper data to generate a second level key, receiving second helper datafrom the non-volatile memory, and performing block decoding on thesecond level key using an error correction code and the second helperdata. The second level key may be generated according to majoritydecision of XORing values of the first helper data and the first levelkey when the bit coding may be performed.

The size of the first level key may be greater than the size of thesecond level key. The size of the second level key may be equal to asize of the third level key, and in some embodiments, the size of thesecond level key may be greater than the size of the third level key.

A physically unclonable function (PUF) circuit according to someembodiments includes a PUF cell array including a plurality of PUFcells, and an error correction unit configured to correct errors in afirst level key output from the PUF cells. The error correction unitincludes a bit encoder configured to perform bit encoding of the firstlevel key using a bit coding table based on Hamming weights to generatesa second level key and to store first helper data corresponding to thesecond level key in a non-volatile memory, and a block encoderconfigured to perform block encoding of the second level key using anerror correction code to generate a third level key and to store secondhelper data corresponding to the third level key in the non-volatilememory.

The first helper data may include at least a part of mask data, and themask data may be determined to generate a predetermined value when a PUFoutput value of each of the PUF cells and a bit value corresponding to akey value according to a Hamming weight of the PUF output value areXORed.

The error correction unit may further include an XOR gate configured toXOR a part of the second level key and the second helper data outputfrom the bit encoder and output an output value. The output value of theXOR gate may be stored in the non-volatile memory,

The error correction unit may further include a bit decoder configuredto perform bit decoding using the bit coding table and the first helperdata read out from the non-volatile memory to correct an error in afirst level key output from each of the PUP cells when the first levelkey may be generated.

The error correction unit may further include a block decoder configuredto perform block decoding using the error correction code and the secondhelper data read out from the non-volatile memory to correct an error ina second level key output from the bit decoder.

BRIEF DESCRIPTION OF THE FIGURES

The above and other objects and features will become apparent from thefollowing description with reference to the following figures, whereinlike reference numerals refer to like parts throughout the variousfigures unless otherwise specified, and wherein

FIG. 1 is a block diagram illustrating a configuration of a PUF circuitaccording to an exemplary embodiment of the inventive concept;

FIG. 2 is a drawing illustrating a 3-bit coding table according to oneexemplary embodiment of the inventive concept;

FIG. 3 is a drawing s rating a 3-bit coding table according to anotherexemplary embodiment of the inventive concept;

FIG. 4 is a drawing illustrating a 3-bit coding table according toanother exemplary embodiment of the inventive concept;

FIG. 5 is a drawing illustrating a 3-bit coding table according toanother exemplary embodiment of the inventive concept;

FIG. 6 is a drawing illustrating a 3-bit coding table according toanother exemplary embodiment of the inventive concept;

FIG. 7 is a drawing illustrating a 3-bit coding table according toanother exemplary embodiment of the inventive concept;

FIG. 8 is a drawing illustrating a 5-bit coding table according to oneexemplary embodiment of the inventive concept;

FIG. 9 is a drawing illustrating a 5-bit coding table according toanother exemplary embodiment of the inventive concept;

FIG. 10 is a block diagram illustrating block encoding without maskingaccording to an exemplary embodiment of the inventive concept;

FIG. 11 is a block diagram illustrating block encoding for performingmasking according to an exemplary embodiment of the inventive concept;

FIG. 12 is a block diagram illustrating key generation according to anexemplary embodiment of the inventive concept;

FIG. 13 is a flowchart illustrating a key enrollment method of a PUFcircuit according to an exemplary embodiment of the inventive concept;

FIG. 14 is a flowchart illustrating a key generation method of a PUPcircuit according to an exemplary embodiment of the inventive concept;

FIG. 15 is a block diagram illustrating a configuration of an electronicdevice according to an exemplary embodiment of the inventive concept;and

FIG. 16 is a drawing illustrating an authentication procedure of a smartcard according to an exemplary embodiment of the inventive concept.

FIG. 17 is a flowchart that illustrates the enrollment of a first levelkey and generation of first helper data.

FIG. 18 is a flowchart that illustrates the generation of a first levelkey or PUFF values and stored helper data.

DETAILED DESCRIPTION

Reference will now be made in detail to the embodiments of the presentgeneral inventive concept, examples of which are illustrated in theaccompanying drawings, wherein like reference numerals refer to the likeelements throughout. The embodiments are described below in order toexplain the present general inventive concept while referring to thefigures. Advantages and features of the present invention and methods ofaccomplishing the same may be understood more readily by reference tothe following detailed description of embodiments and the accompanyingdrawings. The present general inventive concept may, however, beembodied in many different forms and should not be construed as beinglimited to the embodiments set forth herein. Rather, these embodimentsare provided so that this disclosure will be thorough and complete andwill fully convey the concept of the general inventive concept to thoseskilled in the art, and the present general inventive concept will onlybe defined by the appended claims. In the drawings, the thickness oflayers and regions are exaggerated for clarity. Also, the phraseologyand terminology used in this document are for the purpose of descriptionand should not be regarded as limiting. The use of the terms “a” and“an” and “the” and similar referents in the context of describing theinvention (especially in the context of the following claims) are to beconstrued to cover both the singular and the plural, unless otherwiseindicated herein or clearly contradicted by context.

The terms “comprising,” “having,” “including,” and “containing” are tobe construed as open-ended terms (i.e., meaning Including, but notlimited to,”) unless otherwise noted. As should also be apparent to oneof ordinary skill in the art, the systems shown in the figures aremodels of what actual systems might be like. Some of the modules andlogical structures described are capable of being implemented insoftware executed by a microprocessor or a similar device, or of beingimplemented in hardware using a variety of components including, forexample, application specific integrated circuits (“ASICs”). A term like“processor” may include or refer to both hardware and/or software. Nospecific meaning is implied or should be inferred simply due to the useof capitalization. The term “component” or “module”, as used herein,means, but is not limited to, a software or hardware component, such asa field programmable gate array (FPGA) or an application specificintegrated circuit (ASIC), which performs certain tasks. A component ormodule may advantageously be configured to reside in the addressablestorage medium and configured to execute on one or more processors.Thus, a component or module may include, by way of example, components,such as software components, object-oriented software components, classcomponents and task components, processes, functions, attributes,procedures, subroutines, segments of program code, drivers, firmware,microcode, circuitry, data, databases, data structures, tables, arrays,and variables. The functionality provided for the components andcomponents or modules may be combined into fewer components andcomponents or modules or further separated into additional componentsand components or modules. Unless defined otherwise, all technical andscientific terms used herein have the same meaning as commonlyunderstood by one of ordinary skill in the art to which this inventionbelongs. It is noted that the use of any and all examples, or exemplaryterms provided herein is intended merely to better illuminate theinvention and is not a limitation on the scope of the invention unlessotherwise specified. Further, unless defined otherwise, a terms definedin generally used dictionaries may not be overly interpreted.

An issue that arises when implementing a PUF circuit is instability inthe PUF circuit output value. If the bit error rate (BER) of the PUFoutput value is too high, the value may be unusable as a key. Therefore,one of the issues in PUF circuit design is to effectively reduce the biterror rate (BER) of an unstable PUF output value. Although two PUFcircuits may have the same design, the circuits must generate uniquevalues which differ from chip to chip. That is, the value output fromidentical PUF circuits should be different from circuit to circuit. Ingeneral, a PUF circuit generates a unique electronic signature whichdiffers from chip to chip due to process variations during a chipfabrication process. That is, when the transistors that form the circuitare implemented, slight differences in the circuits occur) due tofabrication process variations. However, slight differences duringoperation of the circuit may cause the value output by the PUF circuitto have a considerably high BER. In other words, the output value of aPUF circuit may not be fixed to a certain value, but may have adifferent value due to operating conditions, such as temperature, inputvoltage, aging, etc.

The stability of the PUF output value should therefore be secured inorder to be able to use the PUF output value as an encryption/decryptionkey and/or an authentication code. Many methods of improving PUF circuiterror rates have been proposed. However, because, in general, providingan error correction method in a PUF circuit increases the hardware thatis required to implement the PUF circuit, it is an important limitingfactor for real mass production.

A PUF key enrollment process may be performed once in an initial stageafter a PUF chip is manufactured. Randomly generated keys may be safelystored using a PUF. To correct errors in PUF output values, block-basederror correction coding (i.e., block encoding) and bit-based errorcorrection coding (i.e., bit encoding) may be used together. In aprevious approach, random bits are generate based on a key size. Helperdata generated using the generated random bits are stored in anon-volatile memory. After the key enrollment process is completed, thegenerated random bits may be discarded without being stored in thenon-volatile memory. Keys enrolled through a key enrollment process arerecovered and generated through a key generation process. A key may, forexample, consist of a 128-bit random number. The value of a keysenrolled through a key enrollment process is recovered using PUF outputvalues. Although there may be errors in the PUF output values, i.e., thePUF output values are different from the values which were generated inthe key enrollment stage, the correct PUF output value may be recoveredthrough error correction decoding, such as repetition decoding and/orblock decoding, depending on how the PUF value is encoded.

As noted above, random bits may be used as helper data in a typicalerror correction coding scheme. The amount of helper data which must bestored in a non--volatile memory may be greatly increased as a result ofrepetition coding. Also, generating random bits may result in increasingthe complexity of a system and/or degrading the execution speed of a keyenrollment stage.

An error correction scheme for PUF output values according to someembodiments of the inventive concepts may be implemented to safelyperform repetition coding and block coding without using random bits,which may thereby improve the performance of a PUF system and/or reducethe use of non-volatile memory considerably.

FIG. 1 is a block diagram illustrating a configuration of a PUF circuitaccording to some embodiments of the inventive concepts. Referring toFIG. 1, the PUF circuit 100 may include a PUF cell array 110, an errorcorrection unit 120, and a non-volatile memory (NVM) 130.

The PUF cell array 110 may include a plurality of PUF cells 111 to 11 t(t is an integer greater than or equal to 2). Each of the PUF cells 111to 11 t may be implemented by at least one of a PUF cell based on atransistor threshold voltage, an arbiter-based PUF cell (e.g., anarbiter PUF cell, a feed-forward PUF cell an XOR PUF cell in whicharbiter PUF cells are disposed in parallel, and a lightweight PUF cell),a ring-oscillator-based PUF cell, a memory-based PUF cell (e.g., astatic random access memory (SRAM) PUF cell, a latch PUF cell, a flashmemory PUF cell, and a memistor PUF cell), and a laser- orthermal-reconfigurable PUF cell. In some embodiments of the inventiveconcepts, the PUF cell array 110 may generate a first level key L1_Key.Herein, the first level key L1_Key may include values P1 to Pt, each ofwhich is output from a corresponding one of the PUF cells 111 to 11 t.

In some embodiments of the inventive concepts, the output values P1 toPt of the PUF cells 111 to 11 t may be a plurality of bit values whichare output continuously by the PUF cells. In other embodiments of theinventive concepts, the output values P1 to Pt of the PUF cells 111 tolit may include a plurality of bit values that are output from aplurality of unit cells constituting each of the PUF cells 111 to 11 t.

The error correction unit 120 may include a bit encoder 121 and a blockencoder 122. The error correction unit 120 may generate a second levelkey L2_Key and first helper data HD1 that may be used to correct errorsin the first level key L1_Key. The first helper data HD1 may begenerated by performing bit encoding of the first level key L1_Key usingthe bit encoder 121. Also, the error correction unit 120 may generate athird level key L3_Key and second helper data HD2 that may be used tocorrect errors in the second level key L2_Key. The third level keyL3_Key may be generated by performing block encoding of the second levelkey L2_Key using the block encoder 122.

The bit encoder 121 may receive the first level key L1_Key from the PUFcell array 110, and may generate the second level key L2_Key byperforming bit encoding of the first level key L1_Key. Also, the bitencoder 121 may generate the first helper data HD1 corresponding to thesecond level key L2_Key and may store the first helper data in the NVM130. The bit encoding may be performed, for example, using a bit codingtable based on Hamming weights.

In some embodiments of the inventive concepts, the bit encoder 121 mayreceive output values from the PUF cells 111 to 11 t n times (where n isan integer greater than or equal to 3) and may determine encoded valuesof the PUF cells 111 to 11 k according to Hamming weights (that is, thenumber of bits of “1”) about the output values received n times. Herein,the output values determined by the bit encoder 121 may constitute thesecond level key L2_Key.

To describe generation of a part of the second level key L2_Key of thebit encoder 121, it is assumed that the bit encoder 121 performs 3-bitencoding If three values sequentially output from the first PUF cell 111are “101”, a Hamming weight may be an even number. Accordingly, anoutput value of the first PUF cell 111 may be encoded into “0”. Incontrast, when three values sequentially output from the first PUF cell111 are “001”, the Hamming weight may be an odd number. Accordingly, anoutput value of the first PUF cell 111 may be encoded into “1”. However,the scope and spirit of the Inventive concepts may not be limited to theabove-described bit encoding method. When the Hamming weight is an evennumber, an output value of a PUF cell may be encoded into “1”. When theHamming weight is an odd number, an output value of a PUF cell may beencoded into “0”.

In an exemplary embodiment of the inventive concept, the bit encoder 121may generate the first helper data HD1 corresponding to the second levelkey L2_Key. In an exemplary embodiment of the inventive concept, thefirst helper data HD1 may be data associated with mask data generatedaccording to a variety of bit coding tables.

The block encoder 122 may block encode the second level key L2_Key thatis output from the bit encoder 121 using an error correction code (ECC),and may output a third level key L3_Key as a result of performing theblocking encoding. In some embodiments of the inventive concept, the ECCmay be at least one of a Low Density Parity Check (LDPC) code, a BoseChaudhuri Hocquenghem (BCH) code, a turbo code, a Reed-Solomon code, aconvolution code, a Recursive Systematic Code (RSC), and codedmodulations such as a Trellis-Coded Modulation (TCM) and a Block CodedModulation (BCM). Also, the block encoder 122 may generate second helperdata HD2 corresponding to the third level key L3_Key output byperforming the block encoding, and may store the second helper data HD2in the NVM 130.

The NVM 130 may store the first and second helper data HD1 and HD2. InFIG. 1, an embodiment of the inventive concept is exemplified as the NVM130 is configured in the PUF circuit 100. However, the scope and spiritof the inventive concept may not be limited thereto. For example, theNVM 130 may be configured outside the PUF circuit 100.

The PUF circuit 100 according to an exemplary embodiment of theinventive concept may perform bit coding using a bit coding table basedon Hamming weights without generating random bits.

FIGS. 2 to 11 illustrate a non-exhaustive variety of bit coding tables.

FIG. 2 illustrates a 3-bit coding table according to some embodiments ofthe inventive concepts. Three-bit encoding may be performed according tothe table shown in FIG. 2.

In the table shown in FIG. 2, the first column Pi represents thepossible values of the Level 1 key (L1_Key) output by the ith PUF cell11 i. The second column represents the mask data Mi associated with eachpossible value of the Level 1 key Pi. The third column represents acombination value Ri that is a repeated value of the level 2 key(L2_key) Ki that is output by the bit encoder, while the fourth columnrepresents the value of the L2_Key associated with each value of Pi. Thefifth column represents the helper data Hi which is stored in thenonvolatile memory 130 associated with each possible value of Pi.

For example, referring to the first row of the table shown in FIG. 2,when the output value Pi of a PUF cell is “000”, the Hamming weight isof the output value Pi is “0”. In that case, the key value Ki may be“0”. A combination value Ri is generated by performing 3-bit repetitionencoding on the key value Ki. Thus, for a key value Ki of “0”, therepetition ceded value Ri is “000”.

The mask data value Mi may be a data value that generates thecombination value Ri when the output value Pi of the PUF cell is XORedwith the mask data value Mi (i.e., Ri=Pi XOR Mi). Continuing theprevious example, when the combination value is “000” and the outputvalue Pi is “000”, the mask data value Mi is “000”. The mask data valueMi may be calculated from the output data value Pi and the combinationvalue Ri as Mi=Pi XOR Ri. The helper data value Hi may be set to beequal to the mask data value, in this case “000”.

Similarly, when an output value Pi of a PUF cell is “001” as shown inthe second row of the table shown in FIG. 2, the Hamming weight of theoutput value Pi is “1”. In that case, the key value Ki may be “1”. Thecombination value Ri may therefore be “111” which is obtained byperforming 3-bit repetition encoding of the key value Ki. The mask datavalue Mi, which is a data value for generating the combination value byXORing the mask data value Mi with the output value Pi of the PUF cell,may be “110” in this case. The helper data value Hi may be set as themask data value Mi of “110”.

In general, if bit encoding is performed, because the helper data HD1(refer to FIG. 1) generated for each bit has one bit or more, the secondlevel key L2_Key may be recovered using only the helper data HD1. Asknown in typical repetition coding, a 1-bit error may be recoveredthrough majority decision for a value that results from XORing a valueHi of a helper data HD1 and a PUF output value Pi. In a majoritydecision, if there are more ones than zeros in the data, the result is aone, and if there are more zeros than ones in the data, the result is azero.

As an example, assume that the output values of the first to third PUFcells 111 to 113 are generated as “101.” According to the table in FIG.2, the helper data Hi corresponding to the output values generated inthe key enrollment stage is “101”. Continuing the example, assume a biterror is generated in the output of the first PUF cell 111 during a keygeneration stage. For example, assume that the PUF output value Pigenerated in the key generation stage is “001” instead of the enrollmentvalue of “101.” In that case, when the output value of “001” is XORedwith the helper data of “101,” the resulting value is “100.” Therecovered key value Ki for the PUF output value Pi of “001” is “0”according to majority decision for the XORing value of “100”.

FIG. 17 is a flowchart that illustrates the enrollment of a first levelkey (L1_Key) and generation of first helper data. Referring to FIG. 17,an ith value Pi of PUF data is read from a PUF cell (block S310). TheHamming distance of Pi is calculated, and Ki is set equal to the Hammingdistance of Pi (block S320). A repetition value Ri is then generated byrepeating the value of Ki n times (block S330). A mask value Mi is thengenerated by performing an XOR operation on Pi and Ri, that is, Mi=PiXOR Ri (block S330). The mask value Mi is stored as the ith helper dataHi in a nonvolatile memory (NVM) (block S340).

FIG. 18 is a flowchart that illustrates the generation of a first levelkey (L1_Key) from PUF values and stored helper data. First, a value ofPi is read from the PUF cell (S410). The value of Pi may have errorstherein due to changes in operating conditions of the PUF cell(temperature, aging, etc.) That is, the value of Pi read from the PUFcell may be different from the value that was read from the PUF cellduring the enrollment process.

Helper data Hi corresponding to the ith value Pi is read from thenonvolatile memory (NVM) in which it was stored (block S420). A value ofRi is then calculated as Pi XOR Hi (block S430). The value of Ki maythen be calculated based on a majority vote of the bits in Ri (blockS440).

In case of 3-bit encoding, a size of the PUF output value Pi may be 3times larger than that of the second level key L2_Key. Accordingly, ingeneral, in case of n-bit encoding, the following equation may becalculated using Equation 1.

Size(L1_Key)=n×Size(L2_Key)   [Equation 1]

As shown in FIG. 2, the bit coding table may be configured in a numberof ways. To be safely used in a PUF circuit 100 (refer to FIG. 1), thefollowing two conditions must be satisfied in the bit coding table.

In a first condition, to perform bit decoding using majority decision,an value Ri obtained by XORing the PUF output value Pi with the maskdata value Mi must be a bit stream of (that is, “111”) or a bit streamof ‘0’s (that is, “000”). In a second condition, so that a key value Kicannot be inferred from only a mask data value Mi, a key value Ki ofeither a “0” or a “1” may be obtained with respect to each mask datavalue. For example, in the case when the mask data value Mi is “000”,when a PUF output value is “000”, the key value Ki is “0”, and when aPUF output value Pi is “111” the key value Ki is “1”.

To meet the above-described two conditions, the number of values of themask data values Mi may be a half of the number of PUF output values. Tomeet the first condition, each of the PUF output values Pi maycorrespond to one corresponding mask data value Mi which has the samevalue as each of the PUF output values Pi or has an inverse value of thePUF output values Pi. For example, in the coding table shown in FIG. 2,the mask data value Mi of ‘000’ corresponds to both PUF output values Piof ‘000’ and ‘111,’ the mask data value Mi of ‘110’ corresponds to bothPUF output values Pi of ‘001’ and ‘110,’ etc. Also, to meet the secondcondition, each of the PUF output values Pi may correspond to onecorresponding mask data value Mi which has the same value as each of thePUF output values Pi or has an inverse value of each of the PUF outputvalues Pi. As a result, two PUF output values Pi which have an inverserelation to each other may be configured as one pair. Each of aplurality of pairs may have the same mask data value Mi and may alsohave a mask data value Mi which is different from the other pairs.Accordingly, a space of the mask data values Mi may be a half of a spaceof the PUF output values Pi, thereby representing each of the mask datavalues Mi by only 2 bits.

FIG. 3 illustrates a 3-bit coding table according to other exemplaryembodiments of the inventive concepts. Referring to FIG. 3, 3-bit codingtable has different helper data values Hi compared to the 3-bit codingtable shown in FIG. 2. Each of the helper data values Hi may berepresented by two most significant bits (MSBs) by representing eachmask data values Mi using only 2 bits.

However, the scope and spirit of the inventive concepts may not belimited to the helper data values Hi shown in FIG. 3. For example, thehelper data value Hi may;be represented by one MSB and one leastsignificant bit (LSB).

FIG. 4 illustrates a 3-bit coding table according to further embodimentsof the inventive concepts. Referring to FIG. 4, a 3-bit coding table mayuse different helper data values Hi from the helper values in the 3-bitcoding table shown in FIG. 2. Because mask data values Mi may berepresented by only 2 bits, the helper data value Hi may be representedby one MSB and one LSB of each of the mask data values Mi.

In other embodiments, each of the helper data values Hi may berepresented by two LSBs of corresponding one of the mask data values MLFIG. 5 is a drawing illustrating a 3-bit coding table according tofurther embodiments of the inventive concepts. Referring to FIG. 5, a3-bit coding table may use different helper data values Hi from those inthe 3-bit coding table shown in FIG. 2. Because mask data values Mi maybe represented by only 2 bits, each of the helper data values Hi may berepresented by two LSBs of corresponding one of the mask data values Mi.

Also, as described above, a pair of mask data values Mi may include maskdata values which have an inverse relation to each other. In case ofn-bit encoding, because there are a total of 2n−1 pairs, the number ofencoding schemes which satisfy the above-described conditions may becalculated using Equation 2 as follows:

Number of n bit coding=2⁽² ^(n−1) )   [Equation 2]

Therefore, in case of 3-bit encoding, there may be a total of 16 codingschemes. A bit coding table which has a different type and similarcharacteristics may be configured by inverting the mask data values Mishown in FIG. 2. For example, FIG. 6 is a drawing illustrating a 3-bitcoding table according to further embodiments of the inventive concepts.Referring to FIG. 6, a bit coding table may include inverted mask datavalues Mi compared to the bit coding table shown in FIG. 2. In otherwords, key values Ki determined according to Hamming weights may haveinverted values in comparison with the key values Ki shown in FIG. 2.

FIG. 7 is a drawing illustrating a 3-bit coding table according to stillfurther embodiments of the inventive concepts. Referring to FIG. 7, abit coding table may be different in having helper data values Hi, eachof which has 2 bits, from the bit coding table shown in FIG. 6. Each ofthe helper data values Hi may include two MSBs of corresponding one ofmask data values Mi. Meanwhile, each of the helper data values Hiaccording to some embodiments of the inventive concepts may beimplemented as a variety of helper data values by selecting two bitsamong 3 bits constituting each of the mask data values Mi.

Although the foregoing description is given for the 3-bit coding tablesshown in FIGS. 2 to 7, the scope and spirit of the inventive conceptsmay not be limited to a 3-bit coding table. For example, a bit codingtable according to some embodiments of the inventive concepts may be a5-bit coding table. For example, FIG. 8 illustrates a 5-bit coding tableaccording to some embodiments of the inventive concepts. Referring toFIG. 8, each of the helper data values Hi may use 4 bits except for theLSB of corresponding ones of 5 bit mask data values Mi. Accordingly, thehelper data values Hi according to embodiments of the inventive conceptsmay be implemented as a variety of helper data values by selecting fourbits among the five bits that constitute each of the mask data valuesMi.

FIG. 9 illustrates a 5-bit coding table according to further embodimentsof the inventive concepts. Referring to FIG. 9, a 5-bit coding table mayhave different key values Ki according to Hamming weights in comparisonwith the 5-bit coding table shown in FIG. 8. Therefore, the 5-bit codingtable may be different in mask data values Mi and helper data values Hifrom the 5-bit coding table shown in FIG. 8.

Block coding (or block encoding) is illustrated in FIGS. 10 and 11. FIG.10 is a block diagram illustrating block encoding without maskingaccording to some embodiments of the inventive concepts. Referring toFIG. 10, a block encoder 122 may receive a second level key L2_Key of nbits, may generate a third level key L3_Key of n bits, and may generatesecond helper data HD2 of r bits.

In some embodiments, the second helper data HD2 may not be masked.However, the scope and spirit of the inventive concepts may not belimited to the second helper data HD2. For example, the second helperdata HD2 may be masked to enhance security for the third level keyL3_Key. FIG. 11 is a block diagram illustrating block encoding forperforming masking according to some embodiments of the inventiveconcepts. Referring to FIG. 11, a block encoder 122 may receive a secondlevel key L2_Key of n(=k+r) bits, may generate a third level key L3_Keyof k bits, and may generate masked second helper data HD2 of r bits. AnXOR gate 125 may generate masked second helper data HD2 of r bits byXORing a part (that is, r bits) of the second level key L2_Key and themasked data of r bits of the block encoder 122.

As shown in FIG. 11, because the second helper data HD2 are masked by apart of the second level key L2_Key, there may be no information aboutthe third level key L3_Key, that can be obtained from the second helperdata HD2 alone.

The description is given for the key enrollment method with reference toFIGS. 1 to 11. A description will be given for a key generation methodwith reference to FIG. 12.

FIG. 12 is a block diagram that illustrates key generation according tosome embodiments of the inventive concepts. Referring to FIG. 12, a keygeneration process is described as follows. First of all, it is assumedthat first helper data HD1 and second helper data HD2 are stored in anon-volatile memory (NVM) 130 in the key enrollment process.

In a key generation process, a PUF cell array 110 may output a firstlevel key L1_Key. In other words, PUF cells 111 to 11 t may output PUFoutput values P1 to Pt of t bits. A bit decoder 123 may perform an errorcorrection operation on each of the PUF output values P1 to Pt of t bitsusing the first helper data HD1 that is retrieved from a non-volatilememory (NVM) 130. In the error correction operation, key values Ki(refer to FIG. 2) may be determined according to a majority decision ofthe bits obtained by XORing a PUF output value Pi and a mask data valueMi corresponding to a helper data value Hi. The k key values determinedby the error correction operation may be output as a second level keyL2_Key.

Thereafter, a block decoder 124 may receive the second level key L2_Keyoutput from the bit decoder 123 and the second helper data HD2 from theNVM 130, and may generate a third level key L3_Key by correcting errorsin the second level key L2_Key using a previously determined errorcorrection code. The generated third level key L3_Key may be used as thelast key of a PUF circuit 100.

FIG. 13 is a flowchart illustrating a key enrollment method in a PUFcircuit according to embodiments of the inventive concepts. Referring toFIGS. 1 and 13, a description will be given for a key enrollment methodof the PUF circuit 100 as follows. In step S110, PUF data may begenerated from PUF cells 111 to 11 t. The generated PUF data mayconstitute a first level key L1_Key. In step S120, bit encoding may beperformed using a bit coding table without random bits. A second levelkey L2_Key corresponding to PUF data may be generated as a result of thebit encoding. As shown in FIG. 2, mask data is generated as part of thebit encoding. Therefore, in step S130, first helper data HD1corresponding to the mask data may be stored in the non-volatile memory130. Thereafter, in step S143, block encoding using an error correctioncode may be performed. As a result of the blocking encoding, a thirdlevel key L3_Key and second helper data HD2 associated with the thirdlevel key L3_Key may be generated. In step S150, the second helper dataHD2 may be stored in the non-volatile memory 130, which completes thekey enrollment process of the PUF circuit 100.

In some embodiments of the inventive concepts, the key enrollmentprocess of the PUF circuit 100 may be selectively performed by a user ofan electronic device that includes the PUF circuit 100, or may beperformed by a manufacturer of an electronic device that includes hasthe PUF circuit 100.

FIG. 14 is a flowchart illustrating a key generation method in a PUFcircuit according to some embodiments of the inventive concepts.Referring to FIGS. 12 and 14, a description will be given for a keygeneration method of the PUF circuit 100 as follows. In step S210, PUFdata may be output from PUF cells 111 to 11 t. The PUF data output bythe PUF cells 111 to 11 t may constitute a first level key L1_Key. Instep S220, first helper data HD1 are read out from the non-volatile,memory (NVM) 130. In step S230, bit decoding may be performed using abit coding table without random bits. As a result of performing the bitdecoding, a second level key L2_Key may be generated in which at leastsome errors in the first level key L1_Key are corrected.

Thereafter, in step S240, second helper data HD2 are read out from theNVM 130. In step S250, block decoding using an error correction code maybe performed. As a result of performing the block decoding, a thirdlevel key L3_Key may be generated in which at least some errors in thesecond level key L2_Key are corrected. The generated third level keyL3_Key may be the last key of the PUF circuit 100. Therefore, thegeneration of the PUF circuit may be ended.

In a PUF circuit 100 according to embodiments of the inventive concepts,it may be unnecessary to generate random bits for use in the bitencoding/decoding processes. Moreover, the size of helper data (e.g.,first helper data) used in key error correction may be reduced.Additionally, although there may be a bias in a PUF output value, it ispossible to use coding to improve the bias of a generated keyconsiderably.

A description will now be given for the reason why a key bias of the PUFcircuit may be improved. There are many coding methods for providing nbits. When a proper coding method is selected among selectable codingmethods, a bias of the PUF circuit may be improved.

As shown in FIGS. 3 to 7, a key value Ki may be calculated as a checksumof a PUF output value Pi of 3 bits. In other words, if a Hamming weightof the PUF output value Pi is an even number, a key value Ki is “0”. Ifa Hamming weight is an odd number, a key value Ki is “1”. Assuming thatthe PUF output value Pi is biased by ε, a probability that a given valueof Pi will be generated may be calculated using Equation 3.

Pr(Pi=1)=1/2+ε  [Equation 3]

The bias of the PUF output value Pi may be maintained to a key value Kiwithout change. However, according to the bit coding tables shown inFIGS. 2 to 7, it may be known that the bias of the PUF output value Pimay be improved according to Equation 4.

$\begin{matrix}{\begin{matrix}{{\Pr ( {{Ki} = 1} )} = {{c_{1}^{3}{\bullet ( {Pi}^{1} )}\mspace{11mu} \bullet \mspace{11mu} ( {1 - {Pi}} )^{2}} + {C_{3}^{3}\mspace{11mu} \bullet \mspace{11mu} ({Pi})^{3}\mspace{11mu} \bullet \mspace{11mu} ( {1 - {Pi}} )^{0}}}} \\{= {3\mspace{11mu} \bullet \mspace{11mu} ( \frac{1}{2} )\mspace{11mu} \bullet \mspace{11mu} ( {\frac{1}{2} - ɛ} )^{2}\mspace{11mu} \bullet \mspace{11mu} ( {\frac{1}{2} - ɛ} )^{3}}} \\{= {{3\mspace{11mu} \bullet \mspace{11mu} ( {\frac{1}{8} - {\frac{1}{4}ɛ} - {\frac{1}{2}ɛ^{2}} + ɛ^{3}} )} +}} \\{( {\frac{1}{8} - {\frac{3}{4}ɛ} - {\frac{3}{2}ɛ^{2}} + ɛ^{3}} )\;} \\{= {\frac{1}{2} + {4ɛ^{3}}}}\end{matrix}{ɛ^{\prime} = {{{{\Pr ( {{Ki} = 1} )} - {1/2}}} = {4\; ɛ^{3}}}}} & \lbrack {{Equation}\mspace{14mu} 4} \rbrack\end{matrix}$

Therefore, as a result, a bias ε′ of bit encoding is reduced by ε to thepower of 3.

The foregoing description is given for reducing the bias of the 3-bitencoding shown in FIGS. 2 to 7. In case of 5-bit encoding as shown inFIGS. 8 and 9, a bias of the 5-bit encoding may be reduced more thanthat of the 3-bit encoding. According to the bit coding tables shown inFIGS. 8 and 9, it may be known that the bias is improved according toEquation 5.

$\begin{matrix}{{{\Pr ( {{Ki} = 1} )} = {{{c_{1}^{5}\mspace{11mu} \bullet \mspace{11mu} ({Pi})^{1}\mspace{11mu} \bullet \mspace{11mu} ( {1 - {Pi}} )^{4}} + {C_{3}^{5}\mspace{11mu} \bullet \mspace{11mu} ({Pi})^{3}\mspace{11mu} \bullet \mspace{11mu} ( {1 - {Pi}} )^{2}} + {C_{5}^{5}\mspace{11mu} \bullet \mspace{11mu} ({Pi})^{5}}} = {\frac{1}{2} - {16\mspace{11mu} ɛ^{5}}}}}\mspace{20mu} {ɛ^{\prime} = {{{{\Pr ( {{Ki} = 1} )} - {1/2}}} = {16\mspace{11mu} ɛ^{5}}}}} & \lbrack {{Equation}\mspace{14mu} 5} \rbrack\end{matrix}$

Therefore, as a result, bias ε′ of bit encoding is reduced by to thepower of 5.

FIG. 15 is a block diagram illustrating a configuration of an electronicdevice according to an exemplary embodiment of the inventive concept.Referring to FIG. 15, the electronic device denoted by 1000 may includeat least one processor 1100, a buffer memory 1200, a code memory 1300, aPUF circuit 1400, a cryptographic processing circuit 1500, anon-volatile memory (NVM) interface (1/F) 1600, an NVM 1700, and a hostI/F 1800. Herein, the electronic device 1100 may be one of data storagemedia (e.g., a solid static drive (SSD), a memory stick, and a universalflash storage (UFS) device), memory cards (e.g., a secure digital (SD)card, a multimedia card (MMC), and an embedded MMC (eMMC)), smart cards,mobile devices (e.g., a smart phone and a galaxy tab) and the like.

The processor 1100 may control an overall operation of the electronicdevice 1000. The buffer memory 1200 may be operated under control of theprocessor 1100. The buffer memory 1200 may temporarily store dataprocessed by the processor 1100, and may buffer data transmitted to theNVM 1700 or data read out from the NVM 1700. In an exemplary embodimentof the inventive concept, the buffer memory 1200 may be one of a randomaccess memory (RAM), a static RAM (SRAM), and a phase-change RAM (PRAM).

The code memory 1300 may store codes and/or applications formanaging/operating the electronic device 1000. In an exemplaryembodiment of the inventive concept, the code memory 1300 may be one ofa read only memory (ROM) and a PRAM.

The PUF circuit 1400 may generate keys necessary for security. The PUFcircuit 1400 may be implemented by the PUF circuit 100 shown in FIGS. 1and 12. The PUF circuit 1400 may be implemented by at least one ofhardware, software, and firmware. The PUF circuit 1400 may include a bitgenerator 1410 for generating PUF data and an error correction unit 1420for correcting an error of the generated PUF data. The bit generator1410 may be implemented by the PUF cell array 110 shown in FIG. 1. Theerror correction unit 1420 may include the bit encoder 121 and the blockencoder 122 which are shown in FIG. 1 and the bit decoder 123 and theblock decoder 124 which are shown in FIG. 12.

The cryptographic processing circuit 1500 may perform anencryption/decryption operation of input and output data using a keyvalue output from the PUF circuit 1400.

The cryptographic processing circuit 1500 may transmit and receive datawith and from the NVM 1700 throng h the NVM I/F 1600. The NVM 1700 maybe one of a NAND flash memory, a vertical NAND (VNAND), a NOR flashmemory, a resistive RAM (RRAM), a PRAM, a magnetoresistive RAM (MRAM), aferroelectric RAM (FRAM), a spin transfer torque-RAM (STT-RAM) and thelike. Also, the NVM 1700 may be implemented by a three-dimensional arraystructure.

The host I/F 1800 may be connected with an external host through one ofa parallel AT attachment (PATA) bus, a serial AT attachment (SATA) bus,a small computer system interface (SCSI) a universal serial bus (USB), aperipheral component interconnect express (PCIe), an SD, a serialattached small computer system terrace (SAS), a UFS, an eMMC, an MMC, aNAND interface and the like.

Though not illustrated in FIG. 15, the electronic device 1000 mayfurther include an error correction code (ECC) circuit. The ECC circuitmay generate an ECC for correcting a fail bit or an error bit of datareceived from the NUM 1700, may perform error correction encoding aboutdata provided to the NVM 1700, and may configure data to which a paritybit is added. The parity bit may be stored in the NVM 1700. Also, theECC circuit may perform error correction decoding about data output fromthe NVM 1700. The ECC circuit may correct an error using the parity bit.The ECC circuit may correct an error using one of a Low Density ParityCheck (LDPC) code, a BCH code, a turbo code, a Reed-Solomon code, aconvolution code, a Recursive Systematic Code (RSC), and codedmodulations such as a Trellis-Coded Modulation (TCM) and a Block CodedModulation (BCM).

Though not illustrated in. FIG. 15, the electronic device 1000 may mounta wireless communication function (e.g., wireless-fidelity (Wi-Fi)).

The PUF circuit according to an exemplary embodiment of he inventiveconcept may be applied to a smart card.

FIG. 16 is a drawing illustrating an authentication procedure of a smartcard according to an exemplary embodiment of the inventive concept.Referring to FIG. 16, the smart card denoted by 10 may transmit anidentification (ID) corresponding to a key value generated by a PUFcircuit 12 to a server 20. The PUF circuit 12 may be implemented by thePUF circuit shown in FIGS. 1 and 12. Herein, the ID is a unique value inonly the PUF circuit 12 of the smart card 10. The server 20 may verifywhether the ID of the smart card 10 is registered in a database (DB) 22.When the ID of the smart card 10 is registered in the DB 22, the server20 may generate a challenge corresponding to the ID and may transmit thechallenge to the smart card 10. The smart card 10 may receive thechallenge from the server 20, may generate a response using the PUFcircuit 12, and may transmit the response to the server 20. Therefore,the smart card 10 and the server 20 may safely perform an authenticationprocedure while basically blocking the malicious intent of an attacker.

As described above, a PUF circuit and a key enrollment method thereofaccording to the inventive concepts may perform bit encoding withoutseparate random bits, may reduce a size of helper data, and may reduce abias of an output key by performing bit encoding using a bit codingtable based on Hamming weights of a PUF output value.

While the inventive concept has been described with reference toexemplary embodiments, it will be apparent to those skilled in the artthat various changes and modifications may be made without departingfrom the spirit and scope of the inventive concept. Therefore, it shouldbe understood that the above embodiments are not limiting, butillustrative.

What is claimed is:
 1. A method of performing key enrollment for aphysically unclonable function (PUF) circuit including a plurality ofPUF cells, the method comprising; receiving a first level key from thePUF cells, the first level key comprising a plurality of key values,each of the key values comprising a plurality of bits; performing bitencoding on the first level key using a bit coding table based onHamming weights of the plurality of bits in the key values of the firstlevel key to generate a second level key; storing first helper dataassociated with the second level key in a non-volatile memory;performing block encoding on the second level key using an errorcorrection code to generate a third level key; and storing second helperdata associated with the third level key in the non-volatile memory. 2.The method of claim 1, wherein each of the PUF cells comprises at leastone of a PUF cell based on a transistor threshold voltage, anarbiter-based PUF cell, a ring-oscillator-based PUF cell, a memory-basedPUF cell, and a thermal- or laser-reconfigurable PUF cell.
 3. Themethod, of claim wherein each of the PUF cells comprises a plurality ofunit cells configure to output a plurality of bit vales.
 4. The methodof claim 1, wherein the bit coding table comprises a PUF output valuefor each of the PUF cells, a key value based on a Hamming weight of thePUF output value, a mask data value configured to generate apredetermined value corresponding to the key value when the mask datavalue is XORed with the PUF output value, and a helper data valueassociated with the mask data value.
 5. The method of claim 4, whereinthe predetermined value comprises a bit stream of all bits of “1” or “0”and is configured to correct an error in a PUF output value of each ofthe PUF cells according to a majority decision in a bit decodingprocess.
 6. The method of claim 4, wherein the helper data valuecomprises at least a part of the mask data value.
 7. The method of claim4, wherein the key value is “1” when the Hamming weight is an evennumber, and wherein the key value is “0” when the Hamming weight is anodd number.
 8. The method of claim 4, wherein the key value is “0” whenthe Hamming weight is an even number, and wherein the key value is “1”when the Hamming weight is an odd number.
 9. The method of claim 1,wherein the second helper data is not masked by mask data in the blockencoding.
 10. The method of claim 1, further comprising: masking thesecond helper data using a part of the second level key.
 11. The methodof claim 1, wherein the key enrollment method is initiated in responseto a request of a user to a device including the PUF circuit.
 12. Amethod of performing key generation for a physically unclonable function(PUF) circuit, comprising: receiving a first level key from PUF cells;receiving first helper data from a non-volatile memory; performing bitdecoding on the first level key using a bit coding table based onHamming weights and the first helper data to generate a second levelkey; receiving second helper data from the non-volatile memory; andperforming block decoding on the second level key using an errorcorrection code and the second helper data, wherein the second level keyis generated according to a majority decision of XORing values of thefirst helper data and the first level key when the bit coding isperformed.
 13. The key generation method of claim 12, wherein a size ofthe first level key is greater than a size of the second level key. 14.The key generation method of claim 12, wherein a size of the secondlevel key is equal to a size of the third level key.
 15. The keygeneration method of claim 12, wherein a size of the second level key isgreater than a size of the third level key.
 16. A physically unclonablefunction (PUF) circuit comprising: a PUF cell array including aplurality of PUF cells; and an error correction unit configured tocorrect errors in a first level key output from the PUF cells, whereinthe error correction unit comprises: a bit encoder configured to performbit encoding of the first level key using a bit coding table based onHamming weights to generate a second level key and to store first helperdata corresponding to the second level key in a non-volatile memory; anda block encoder configured to perform block encoding of the second levelkey using an error correction code to generate a third level key and tostore second helper data corresponding to the third level key in thenon-volatile memory.
 17. The PUF circuit of claim 16, wherein the firsthelper data comprises at least a part of mask data, wherein the maskdata are determined to generate a predetermined value when a PUF outputvalue of each of the PUF cells and a bit value corresponding to a keyvalue according to a Hamming weight of the PUF output value are XORed.18. The PUF circuit of claim 16, wherein the error correction unitfurther comprises: an XOR gate configured to XOR a part of the secondlevel key and the second helper data output from the bit encoder andoutput an output value, wherein the output value of the XOR gate isstored in the non-volatile memory.
 19. The PUF circuit of claim 16,wherein the error correction unit further comprises: a bit decoderconfigured to perform bit decoding using the bit coding table and thefirst helper data read out from the non-volatile memory to correct anerror in a first level key output from each of the PUF cells when thefirst level key is generated.
 20. The PUF circuit of claim 19, whereinthe error correction unit further comprises: a block decoder configuredto perform block decoding using the error correction code and the secondhelper data read out from the non-volatile memory to correct an error ina second level key output from the bit decoder.